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Making Sense of the IMF Quota Formula

Edwin M. Truman (Former PIIE)



The formula employed by the International Monetary Fund (IMF) and its members to help guide the distribution of the Fund's quota subscriptions and voting power is one of the more arcane topics in international finance.1  But it is also a proxy for many large and important zero-sum issues, such as which countries are up and which countries are down, which countries should call the shots and which countries should not, and which countries deserve support and which do not.2 At stake, then, is nothing less than how economic power is to be distributed and recognized among emerging market, developing, and developed countries.

In this piece, I attempt to make sense of the discussion about revising the quota formula. I recommend a simple formula based on GDP and, if necessary, variability of current receipts and payments. I am consistent; I made a similar recommendation in Reforming the IMF for the 21st Century (Truman 2006).

Having revised the quota formula in 2008 to no country's satisfaction, the members of the IMF agreed in 2010 to try again.3 Their target was to reach agreement on a revised formula by January 2013 so that it could be used as part of a review of IMF quotas to be completed by January 2014. The other 2010 decisions on IMF quotas and governance reforms are yet to be implemented. They are unlikely to be implemented before the end of this year because of the Obama administration's decision not to submit the necessary legislation to a US Congress in continued gridlock. Consequently, the best bet is that any reform of the IMF quota formula will be rolled into the 2014 decision on whether to increase IMF quotas and, if so, by how much and in what manner. But it is useful to lay some groundwork for those decisions.

It is no surprise that, following the IMF executive board's first, formal discussion of the quota formula on July 19, 2012, the IMF released a summary stating that the directors had expressed a "wide range of views," while not providing many details (IMF 2012a). On the other hand, the executive board, management, and staff are to be congratulated for promptly releasing the underlying documents and data, an improvement over past practice.

The review of the quota formula is supposed to produce an agreement on a formula that "better reflects members' relative positions in the global economy" (IMF 2012a). Moreover, the formula is expected to be simple and transparent. Logically, most economists would agree that the single, best measure of a country's relative position in the global economy is its gross national product (GDP). Indeed, the IMF executive board generally agrees with this proposition. But what do we mean by GDP? Should the focus be on GDP at market exchange rates or on purchasing-power-parity (PPP) exchange rates, adjusted for the higher effective purchasing power of a dollar in lower-income countries, which would effectively translate into greater buying power for China and most other developing countries?

Based on data through 2010, the existing quota formula produces a calculated quota share for the United States of 15.8 percent, while its actual quota post-2010 agreement will be 17.4 percent, and its blended GDP share in the formula is 22.2 percent. The blend is an average of 60 percent of the US share of GDP at market exchange rates (23.6 percent) and 40 percent of the US share of GDP at PPP exchange rates (20.1 percent). Thus, the US quota share is significantly less than its blended GDP share, and its GDP share at market exchange rates is somewhat larger than its GDP share at PPP exchange rates. But these differences are much starker for the other six G-7 countries, which have a combined calculated quota share of 24.8 percent. That amount is slightly less than their blended GDP share of 25.2 percent and their share of GDP at market exchange rates of 28.4 percent. But it is substantially larger than their share at PPP exchange rates of 20.5 percent.

In the long run, GDP on a PPP basis should converge to GDP at market exchange rates. Therefore, one approach to making the formula simple is to base it solely on GDP with as large a weight on PPP-based GDP as is politically acceptable to countries yielding their shares.  

The problem is that, although it is agreed that the formula should be simple and transparent and that GDP is the best single variable reflecting relative positions in the global economy, the adversely affected countries do not want their quota shares to be reduced from the status quo. These countries would include, in particular, European members of the IMF. But the scorekeeping is complex. Moreover, the scorekeeping is distorted by a narrow focus on out-of-date categories of advanced countries and emerging market and developing countries.

In the aggregate, adopting the current blend of GDP as the sole variable in the quota formula would not disrupt the balance between advanced countries and emerging market and developing countries compared with the status quo following the 2010 agreements. The advanced country share would increase by 0.6 percentage points and the share of the emerging market and developing countries would be reduced by the equal amount.4 In the broader scheme of things, this rearrangement would soon disappear. According to IMF staff projections, between 2010 and 2017, the share of emerging market and developing countries in PPP-based global GDP will rise by 6.4 percentage points.5 Moreover, based on data through 2010, the combined quota share of the European Union would decline 4.9 percentage points relative to the status quo, from 30.2 percent to 25.3 percent.6

One distressing flaw in the way the IMF executive board requires the staff to present these comparisons is that the classification of countries as advanced countries or as emerging market and developing countries is out of date. Consequently, although Korea and Singapore are now classified in the IMF's World Economic Outlook as advanced economies, for these purposes they are classified as emerging market economies. In addition, some members of the European Union are still classified as emerging market (transition) countries even though some of them, such as Estonia, the Slovak Republic, and Slovenia, have joined the euro area, and, by construction, are classified as advanced countries in the World Economic Outlook.

Also potentially troublesome is the fact that moving to a GDP-only approach would reduce quota shares for a large proportion of members of the IMF if the new formula were fully implemented immediately, rather than stretched out over a decade or more. Twenty-five of the 35 members with the largest quota shares under the status quo, those with shares of 0.515 percent or more after the 2010 agreement goes into effect, could anticipate such a decline. And this number only declines to 21 countries if the GDP variable were PPP based.7 For the next 35 members, with quota shares between 0.148 percent and 0.509 percent, the numbers are even higher—32 and 28 members respectively.8 From my perspective, these changes result from historical distortions introduced into quotas and the quota formula by largely extraneous variables. These problems illustrate the difficulty of getting broad acceptance for radical changes in the quota formulas. Nevertheless, my task is to set a high bar.

For some, the most troubling aspect of adopting a quota formula involving only one or more GDP variables is that the formula would reduce the quota shares of the low-income members of the IMF, defined as the 71 countries eligible to borrow from its Poverty Reduction and Growth Trust (PRGT). However, that would be true of almost any change from the status quo. Under the 2010 agreement, these countries will have a combined share of IMF quotas of 4.0 percent, but their combined calculated quota share implied by the current quota formula is 2.7 percent, and their share of any of the current four quota variables ranges between 2.1 percent for openness and reserves to 2.2 percent for the GDP blend and 2.6 percent for variability (IMF 2012b). The argument in favor of such a step is about political cosmetics. One could reasonably ask what practical consequences would result from adding, say, 5 percentage points to the collective quota share of this group of countries, an average of 0.07 percentage points per member. No country's voice in the IMF would be increased significantly. These countries are not financial contributors to the IMF. In principle, with higher quota shares, they would become eligible to borrow more from the IMF, because the size of programs is linked to the size of quotas. However, it would be more straightforward, instead, to adjust the average size of programs for these countries on the assumption that the PRGT had the financing. This would avoid distorting the quota structure as countries graduate from PRGT eligibility.

An alternative solution would be to revamp the vulnerability variable in the quota formula to favor this group of countries. The underlying argument for a variable based on the variability of current receipts and net capital flows is that such a variable reflects a potential need to borrow from the IMF. One might reasonably surmise that this need was particularly relevant for low-income members. In IMF (2009), the staff of the IMF reviewed a number of alternative formulations of the variability element in the quota formula. They concluded that none of the candidates, save a composite variable, is significantly correlated with borrowing from the IMF and added that "small countries tend to have the largest shares under this approach." However, many, but not all, small countries are also low-income countries. As of 2009, if the traditional variability element were scaled by GDP, what Ralph Bryant (2010) calls a ratio-share variable—in contrast with a level-share variable—the IMF staff estimated that the share for the advanced countries would be 8.6 percent, the share for the emerging market and developing countries would be a corresponding 91.4 percent, but the share for the low-income countries would be 50.2 percent.

It follows that if low-income countries must be favored via the quota formula for political reasons, a reasonable approach would be a quota formula in which 90 percent was devoted to a GDP level-share variable and 10 percent to variability in ratio-share form. This would produce a combined quota share of about 7.5 percent for the low-income countries, importantly without the use of gimmicks, compared to their current artificial share of 4.0 percent (post 2010 agreement). The emerging market and developing countries would have a share of about 47 percent, compared with their current 42.4 percent. The advanced countries would have a combined share of about 53 percent, compared with their current 57.6 percent. The US share would rise to about 20 percent from the current 17.4, but the European Union share would decline to about 24 percent from the current 30.2 percent.9

Turning to the broader issue of including variables other than GDP in the quota formula, what is troubling about the treatment of variability in IMF 2009 is that the IMF staff goes to great lengths to demonstrate that simple forms of this variable are uncorrelated with the need to borrow from the IMF. To my knowledge, the IMF staff has never performed similar exercises with the other two variables in the current formula, so-called openness and reserves.

The "openness" variable is another proxy for a country's potential need to borrow from the IMF.10 The IMF staff should investigate whether this variable in any form is correlated with the need to borrow from the IMF. I would be very surprised if they came up with a positive result.

In a similar vein, the logic behind the reserves variable in the current quota formula is that it reflects a country's capacity to lend to the IMF. Why has the IMF staff never tested this proposition? Again, my strong prior is that they would find no correlation between the level of a country's reserves and its actual participation in lending to the IMF.

Bryant (2010) and a few other commentators have advocated including a population variable in the quota formula. Bryant invokes the analogy of the democratic principle of one person and one vote. Population, of course, is indirectly included via any GDP variable because GDP can be measured as GDP per capita times population. But introducing population as a consideration creates new complexities. Singapore, for example, had an estimated 2011 GDP on a PPP basis giving it a rank of 39 because its GDP per capita ranked 3 despite the fact that its population ranked 112. China had a GDP ranked 2 although its GDP per capita ranked only 96 because its population ranked 1. Population is more skewed than GDP. The top 10 countries in population account for 59 percent of the world total, but the top 10 countries in GDP account for only 22 percent. The bottom 10 countries in population have only 0.016 percent of the total but the bottom ten countries in GDP have a whopping 0.25 percent of the total.11

I am agnostic about the inclusion of population the IMF quota formula. There is a philosophical case for doing so, but doing so would add another complexity to the formula discussions. Another variable would imply that the IMF quota formula should be designed to reflect even more considerations than at present, and my sense is that the formula is already over burdened. Nevertheless, the IMF executive board should decide if they want the staff to explore the implications of including this variable in the formula or explain why not.

In conclusion, my advice to the members of the IMF is to adopt a formula based on level-shares of GDP. In deciding the proportions between GDP at market versus PPP exchange rates, apply Henry Wallich's law: When you want to know how many cats and dogs there should be on the moon, assume that there should be an equal number. If political considerations dictate tilting the formula toward the low-income countries, add variability as a ratio share to GDP. In addition, drop the compression factor. It needlessly complicates the formula, notionally to the benefit of the low-income countries, but de facto to the benefit of the upper middle income countries—largely located in Europe—which are already over-represented in the IMF. Keep the formula simple and transparent.


This piece is based on remarks delivered at a Brookings-CIGI-G24 High Level Seminar on quota reform held at the IMF on August 30, 2012.

Bryant, Ralph C. 2010. Governance Shares for the International Monetary Fund: Principles, Guidelines, Current Status (April 20). Available at

Cooper, Richard N. and Edwin M. Truman. 2007. The IMF Quota Formula: Linchpin of Fund Reform. PIIE Policy Brief 07-01. Washington: Peterson Institute for International Economics.

IMF (International Monetary Fund). 2009. Quotas—Updated Calculations and Quota Variables (August 27). Washington. Available at

IMF (International Monetary Fund). 2012a. IMF Executive Board Discusses Quota Formula Review. Public Information Notice No. 12/94 (August 2). Washington. Available at

IMF (International Monetary Fund). 2012b. Quota Formula Review—Data Update and Further Considerations (June 28). Washington. Available at

Truman, Edwin M. 2006. Rearranging IMF Chairs and Shares: The Sine Qua Non of IMF Reform. In Reforming the IMF for the 21st Century, ed. Edwin M. Truman. Washington: Peterson Institute for International Economics.

1. The IMF quota formula is an arcane topic for several reasons: First, it involves many technical data issues. Second, it only becomes relevant if there is a decision to increase IMF quotas, which are advance commitments to provide financial resources to the IMF. Third, even if it is decided to increase IMF quotas, the formula may or may not play a significant role in the actual distribution of additions to existing quotas.

2. When the 2010 agreement is implemented, the US quota share in the IMF will be 17.4 percent and the US voting share will be 16.5 percent, giving the United States alone an effective veto over certain major IMF decisions. At the same time, the combined quota share of the 27 countries in the European Union will be 30.2 percent and their combined voting share will be 29.4 percent. Most countries believe that Europe is vastly over-represented in the IMF. The European Union is not 75 to 80 percent larger economically or financially than the United States.

3. The current quota formula, adopted in 2008 after more than a decade of debate, is a linear combination of 50 percent of a country's share of GDP (60 percent at market and 40 percent at PPP exchange rates), 30 percent of a country's share of "openness" (mischaracterized as the average of current payments and receipts), 15 percent of a country's share of the variability of current receipts and net capital flows (measured as the standard deviation from a centered three-year trend over a 13-year period), and 5 percent of a country's share of official reserves on average over a yea, all raised to the power 0.95 (compression factor) and rescaled so that the sum of all quota shares equals 100. All variables are expressed as level-shares in which each country's share is equal to the value of the variable, for example GDP, relative to the total for all countries.

4. Retaining the compression factor, which I do not favor, would reverse this result. The combined share of the advanced countries, in this case, would decline by 1.1 percentage points, compared with the status quo, under a pure GDP formula with the current blend and the emerging market and developing countries would see their combined share rise by that amount.

5. The IMF projects that the emerging market and developing countries share of PPP-based global GDP will exceed 50 percent in 2013. Source: World Economic Outlook database of April 2012 available at

6. At the same time, the US share would rise from 17.4 percent under the status quo, which includes the effect of the irrational compression factor, to 22.2 percent, but it should be noted that any adjustment would take several quinquennial quota reviews before reaching full effect by which time the size of the total adjustment would be substantially reduced if not eliminated. For example, the US share of PPP-based global GDP is projected to decline by 1.7 percentage points between 2010 and 2017. Over the same period, the European Union's share is projected to decline by 3.3 percentage points.

7. Source: Updated IMF Quota Data—August 2012.

8. A comparison with calculated quotas under the current formula using data through 2010 produces similar results.

9. I use the word "about" in these calculations because I am combining results from IMF 2009 with results from IMF 2012b, and these two papers employ different data sets. However, I am confident about the direction of my results.

10. The variable is mis-specified as a level-share variable when it should be specified as a ratio-share variable if used at all. Richard Cooper and I argued (Cooper and Truman 2007) that the case for including this variable at all is very weak.

11. These data are from the World Economic Outlook database of April 2012.

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